Fujita’s freeness conjecture predicts that if X is a smooth projective variety and A is an ample divisor on X, then K+mA is basepoint-free when m is at least dim(X)+1. Although this statement is optimal (as can be seen when X is projective space) there are much better statements for abelian varieties and surfaces with numerically trivial canonical bundle. In this talk, I will discuss a result of Fujita type for smooth projective varieties having numerically trivial canonical bundle, as well as its application to moduli spaces of sheaves on abelian surfaces. This is joint work with Alex Kuronya.